Knowledge graphs represent known facts using triplets. While existing knowledge graph embedding methods only consider the connections between entities, we propose considering the relationships between triplets. For example, let us consider two triplets $T_1$ and $T_2$ where $T_1$ is (Academy_Awards, Nominates, Avatar) and $T_2$ is (Avatar, Wins, Academy_Awards). Given these two base-level triplets, we see that $T_1$ is a prerequisite for $T_2$. In this paper, we define a higher-level triplet to represent a relationship between triplets, e.g., $\langle T_1$, PrerequisiteFor, $T_2\rangle$ where PrerequisiteFor is a higher-level relation. We define a bi-level knowledge graph that consists of the base-level and the higher-level triplets. We also propose a data augmentation strategy based on the random walks on the bi-level knowledge graph to augment plausible triplets. Our model called BiVE learns embeddings by taking into account the structures of the base-level and the higher-level triplets, with additional consideration of the augmented triplets. We propose two new tasks: triplet prediction and conditional link prediction. Given a triplet $T_1$ and a higher-level relation, the triplet prediction predicts a triplet that is likely to be connected to $T_1$ by the higher-level relation, e.g., $\langle T_1$, PrerequisiteFor, ?$\rangle$. The conditional link prediction predicts a missing entity in a triplet conditioned on another triplet, e.g., $\langle T_1$, PrerequisiteFor, (Avatar, Wins, ?)$\rangle$. Experimental results show that BiVE significantly outperforms all other methods in the two new tasks and the typical base-level link prediction in real-world bi-level knowledge graphs.

翻译：知识图谱通过三元组表示已知事实。现有的知识图谱嵌入方法仅考虑实体间的连接，而本文提出考虑三元组之间的关系。例如，考虑两个三元组 $T_1$ 和 $T_2$，其中 $T_1$ 为（奥斯卡奖，提名，阿凡达），$T_2$ 为（阿凡达，获奖，奥斯卡奖）。给定这两个基础层三元组，我们发现 $T_1$ 是 $T_2$ 的前提条件。本文定义高层三元组来表示三元组间的关系，如 $\langle T_1$，前提条件，$T_2\rangle$，其中“前提条件”是高层关系。我们构建了包含基础层和高层三元组的双层知识图谱，并提出基于双层知识图谱随机游走的数据增强策略来补充合理的三元组。所提模型 BiVE 通过同时考虑基础层和高层三元组结构以及增强三元组来学习嵌入。我们提出两个新任务：三元组预测和条件链接预测。给定三元组 $T_1$ 和某个高层关系，三元组预测将预测可能通过该高层关系与 $T_1$ 关联的三元组，例如 $\langle T_1$，前提条件，?$\rangle$；条件链接预测则预测以另一三元组为条件的三元组中缺失的实体，例如 $\langle T_1$，前提条件，(阿凡达，获奖，?)$\rangle$。实验结果表明，在真实世界双层知识图谱上，BiVE 在这两个新任务及典型的基础层链接预测中均显著优于其他方法。